A carpenter has several boards of equal length. He cuts 3\/5 of each board. After cutting the boards, the carpenter notices he has enough pieces left over to make up the same length as 4 of the original boards. How many boards did the carpenter start with?<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To solve this problem, let\u2019s define the variables and carefully work through the logic:<\/p>\n\n\n\n Let each board have a total length of 1 unit<\/strong> (for simplicity).<\/p>\n\n\n\n The carpenter cuts 3\/5<\/strong> of each board, which means 2\/5 of each board remains<\/strong>.<\/p>\n\n\n\n Let x<\/strong> be the number of original boards.<\/p>\n\n\n\n So, the leftover piece from each board is 2\/5<\/strong> units in length.<\/p>\n\n\n\n If the carpenter starts with x<\/strong> boards, then the total leftover length<\/strong> is: x\u00d725x \\times \\frac{2}{5}<\/p>\n\n\n\n We’re told that this leftover total length is equal to 4 full boards<\/strong>, or simply 4 units<\/strong> in total.<\/p>\n\n\n\n x\u00d725=4x \\times \\frac{2}{5} = 4<\/p>\n\n\n\n x=4\u00d752=202=10x = \\frac{4 \\times 5}{2} = \\frac{20}{2} = 10<\/p>\n\n\n\n To find out how many boards the carpenter started with, we begin by interpreting the key information. Each board is cut so that 3\/5 is removed<\/strong> and 2\/5 is left<\/strong>. The crucial piece of information is that the total leftover wood<\/strong>\u2014which consists of the 2\/5 segments from each board\u2014adds up to the equivalent of 4 full boards<\/strong>.<\/p>\n\n\n\n For ease of calculation, we assume each board is 1 unit long. This makes it simple to calculate fractions of the board. If each board is 1 unit, then cutting off 3\/5 leaves 2\/5 of a unit per board. So, every time the carpenter cuts a board, he has 2\/5 of a board left.<\/p>\n\n\n\n Let x<\/strong> represent the number of boards the carpenter starts with. From each of the x boards, there remains 2\/5 of a board. Therefore, the total leftover length is x \u00d7 2\/5<\/strong>.<\/p>\n\n\n\n We are told that all the leftover pieces combined are equal in length to 4 full boards (i.e., 4 units). So we can write the equation: x\u00d725=4x \\times \\frac{2}{5} = 4<\/p>\n\n\n\n Multiplying both sides by 5 to eliminate the denominator: 2x=202x = 20<\/p>\n\n\n\n Dividing both sides by 2: x=10x = 10<\/p>\n\n\n\n So, the carpenter originally had 10 boards<\/strong>. This problem is a classic example of how fractions and simple algebra can be applied to real-life situations to determine totals when parts are removed or left behind.<\/p>\n","protected":false},"excerpt":{"rendered":" A carpenter has several boards of equal length. He cuts 3\/5 of each board. After cutting the boards, the carpenter notices he has enough pieces left over to make up the same length as 4 of the original boards. How many boards did the carpenter start with? The Correct Answer and Explanation is: To solve […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-214539","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/214539","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=214539"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/214539\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=214539"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=214539"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=214539"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nLet\u2019s Define the Variables:<\/strong><\/h3>\n\n\n\n
\n\n\n\nSet up the Equation:<\/strong><\/h3>\n\n\n\n
\n\n\n\nSolve for x:<\/strong><\/h3>\n\n\n\n
\n\n\n\n\u2705 Correct Answer: 10 boards<\/strong><\/h3>\n\n\n\n
\n\n\n\n300-Word Explanation:<\/strong><\/h3>\n\n\n\n